PRP Records

Probable Primes Top 10000

(172751 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 30000) Who ? When ?
8001(6^71345-61)/555517Lelio R Paula05/2014
80022^184407-301955513Yves Minet10/2014
8003(43*10^55512-61)/955513Robert Price06/2015
800420^42667-84355512Enzo Doria03/2013
8005133^26134-13255505Norbert Schneider03/2015
8006(31*2^184378-1)/71155502Lelio R Paula01/2014
80079*7^65667-455497Lelio R Paula09/2014
80082^184342-17355493Lelio R Paula03/2011
800915^47182+9255491Lelio R Paula02/2013
80105^79378+655483Lelio R Paula10/2012
8011581^20068+20068^58155472Norbert Schneider06/2016
8012(2^184232+1)/25755457Donovan Johnson03/2005
801318^44177-141555455Enzo Doria03/2013
80142^184203-279786755451Enzo Doria04/2016
80152^184189+1755447Lelio R Paula03/2011
80162^184183+2612355445Yves Minet01/2010
8017Phi(77077,10)55441Ray Chandler05/2009
80182^184141-11325155432Enzo Doria07/2014
80192^184093-50461355418Gary Barnes09/2009
8020(lucasV(1,2,368167)+2)/(11*1103*1307*5647)55404Mike Oakes04/2017
80212^184044-11126955403Enzo Doria05/2014
802214051^8766+8766^1405155401Hans Havermann07/2016
802398^27819+27819^9855394Serge Batalov05/2014
802458046^9+9^5804655390Andrey Kulsha02/2004
80252^183980+7524155384Enzo Doria04/2016
802610^55372+3755373Robert Price01/2011
802710^55372-4996755372Patrick De Geest12/2012
8028(13*10^55367+17)/355368Robert Price06/2015
80292*6^71150+755366Lelio R Paula09/2014
803019^43296-6255365Lelio R Paula02/2013
803119^43295+1055364Lelio R Paula02/2013
8032(29*10^55362-11)/955363Robert Price04/2015
8033(37*10^55359+53)/955360Robert Price05/2015
803419^43283+7255349Lelio R Paula02/2013
80352^183800-6555330Lelio R Paula03/2011
803621001^12801-11055329Enzo Doria07/2012
803733^36433-32^3643355325Robert Price04/2012
8038(17*2^183729+1)/14555308Lelio R Paula07/2012
80409^57952+8^(57952-1)55301Robert Price03/2016
803914872^5229+5229^1487255301Hans Havermann08/2016
804161^30972-255296Lelio R Paula08/2013
80422^183671-11253755291Enzo Doria06/2014
8043(2^183687+7)/49793974555287Lelio R Paula02/2012
80443^115873+5655286Lelio R Paula10/2012
804513^49629-8455284Lelio R Paula01/2013
80462^183632-555279Henri Lifchitz08/2005
804713981^8988+8988^1398155277Hans Havermann07/2016
8048(5*2^183585+1)/1355265Lelio R Paula07/2012
80492^183576+17155262Lelio R Paula03/2011
805013^49604+8255257Lelio R Paula01/2013
8051(11*10^55254+1)/355255Erik Branger03/2014
80523^115802-2655252Lelio R Paula10/2012
80532^183534-364555250Lelio R Paula01/2011
8054(15*2^183533-1)/11355249Lelio R Paula01/2014
80555^79032-1376655241Enzo Doria02/2013
80568*3^115759-755232Lelio R Paula03/2014
80576^70974-13755229Lelio R Paula10/2012
80582^183446-11307355223Enzo Doria07/2014
80592^183441+57729457555222Lelio R Paula03/2013
80605^79000-655219Lelio R Paula10/2012
80612^183413-90155213Yves Minet01/2012
806219^43168-5055202Lelio R Paula02/2013
80632^183340+1968355191Lelio R Paula02/2012
80646^70923+3555189Lelio R Paula10/2012
80652^183317-403555184Lelio R Paula01/2011
80662^183284-1555174Lelio R Paula03/2011
80672^183255+14955166Lelio R Paula02/2011
80684*10^55165+8755166Robert Price05/2016
8069(3^115574+4)/6303755139Lelio R Paula03/2012
80702^183165-11233355139Enzo Doria06/2014
80712^183142+85555132Lelio R Paula01/2011
8072(49*10^55129+383)/955130Robert Price04/2017
80732^183019+25525555095Lelio R Paula01/2011
80743*10^55077+755078Erik Branger11/2013
8075(62*10^55075-71)/955076Robert Price09/2015
807627499!2-3255070Robert Price10/2015
807715307^3958+3958^1530755067Hans Havermann08/2016
807870^29836-6955051Norbert Schneider10/2012
807918^43854-8355049Lelio R Paula02/2013
80807^65126+5855038Lelio R Paula10/2012
80812^182827-161555037Lelio R Paula11/2009
80827*10^55030-955031Dmitry Domanov11/2010
80836^70702+2355017Lelio R Paula10/2012
8084(23*2^182753+1)/15155014Lelio R Paula07/2012
80852^182743-161555012Lelio R Paula11/2009
8086(24737*2^182736+1)/39955011Lelio R Paula05/2014
80873^115280-956855003Enzo Doria02/2013
80882^182656-1284954985Enzo Doria10/2012
80899*19^42995+1654981Curtis Bright05/2015
80902^182627+2842554977Lelio R Paula11/2009
80912^182597-11305354968Enzo Doria07/2014
8092(3^115213+2)/3090672554964Lelio R Paula03/2012
80932^182581-197554963Yves Minet09/2012
809427449!!-1654959Robert Price06/2015
80964^91283-3^9128354958Jean-Louis Charton01/2004
80952^182565+10754958Lelio R Paula11/2009
80972^182560+205354957Lelio R Paula12/2010
80982^182451-18245154924Henri Lifchitz10/2004
80992^182444+8154922Henri Lifchitz10/2005
81002^182433+7410554918Enzo Doria04/2016
810120^42206-524354912Enzo Doria03/2013
81022^182394+8554907Lelio R Paula02/2011
81032^182374-11228754901Enzo Doria06/2014
8104(47^32833-33^32833)/1454899Serge Batalov12/2016
81052^182363-11316754897Enzo Doria07/2014
81062^182359-11222154896Enzo Doria06/2014
8107(F(1905)^139-F(1904)^139)/F(1903)54893Wayne Halsdorf05/2010
8108(17*2^182274+1)/146754869Lelio R Paula01/2012
810918^43698-554853Lelio R Paula02/2013
81102^182209-189354851Yves Minet09/2012
81112^182194-344354846Yves Minet12/2016
811215023^4468+4468^1502354836Hans Havermann08/2016
81132^182135+9014354829Yves Minet10/2010
81142^182119+7433354824Enzo Doria04/2016
811514289^6860+6860^1428954818Hans Havermann08/2016
81163^114892-114892^354818Norbert Schneider03/2017
81172^182070-4735554809Lelio R Paula01/2011
81183^114869+7654807Lelio R Paula10/2012
81198^60681-60681^854801Norbert Schneider12/2016
81201897^16710+16710^189754777Serge Batalov05/2014
8121Phi(61868,59)54776Enzo Doria04/2012
8122113^26679+254775Lelio R Paula05/2013
81233^114789-7454769Lelio R Paula10/2012
812415^46567+9854768Lelio R Paula02/2013
8125(2*10^54767-71)/354767Robert Price01/2017
8126(21*2^181931-1)/16999754763Lelio R Paula01/2014
81272^181913+2954762Henri Lifchitz06/2005
8128(31*10^54761-121)/954762Robert Price06/2016
81292^181887+18954754Lelio R Paula02/2011
81302^181874+181874^2-154750Robert Price04/2014
8131(2^181865+9)/733954743Lelio R Paula02/2012
81325^78314-9254740Lelio R Paula10/2012
8133(163*10^54727-1)/954729Serge Batalov12/2014
813415^46531+7454725Lelio R Paula02/2013
8135277^22400-34854712Enzo Doria07/2012
81366^70302+10154706Lelio R Paula10/2012
81373^114622-1040854689Enzo Doria02/2013
8139(23*2^181674+1)/48954688Lelio R Paula01/2012
81382^181669-155154688Yves Minet08/2012
8140(57352^11491-1)/5735154676Serge Batalov04/2015
8141(31*2^181629-1)/1073472154671Lelio R Paula01/2014
8142(F(1048)^251-F(1047)^251)/F(1046)54668Wayne Halsdorf05/2010
814313^49073+4654665Lelio R Paula01/2013
8144(57042^11491-1)/5704154649Serge Batalov04/2015
814620^42000+7354644Lelio R Paula02/2013
8145(67607*2^181517+1)/165554644Lelio R Paula05/2014
814733*10^54634+754636Robert Price07/2016
814820^41988+6154628Lelio R Paula01/2013
814920^41988-812354628Enzo Doria03/2013
81502^181420+2118154613Yves Minet03/2011
8151(19*10^54608+161)/954609Robert Price07/2016
815219^42696-2454598Lelio R Paula02/2013
8153(74*10^54583+61)/954584Robert Price10/2015
81542^181316-9439554582Lelio R Paula09/2011
815514751^5006+5006^1475154572Hans Havermann08/2016
815614^47609+3954567Lelio R Paula02/2013
81573^114327-7454548Lelio R Paula10/2012
8158gcd(V(995625),5*F(199125)*(F(199125)-1)+1)54546Serge Batalov04/2015
81592^181155-1155*18115554534Henri Lifchitz02/2005
8160Phi(61672,83)54533Enzo Doria05/2012
81619*2^181128+754526Lelio R Paula03/2014
816289*10^54518-754520Robert Price03/2017
81632^181090-11324754514Enzo Doria07/2014
816414031^7670+7670^1403154508Hans Havermann08/2016
816514210^6849+6849^1421054505Hans Havermann08/2016
81662^181043-19954500Lelio R Paula02/2011
816712^50499+554498Lelio R Paula01/2013
816812^50491+554489Lelio R Paula01/2013
81696^70016-14554484Lelio R Paula10/2012
817011^52313-960054479Enzo Doria02/2013
81712^64459+3^64459+5^64459+7^6445954475Henri Lifchitz08/2001
81722^180946-11104154471Enzo Doria05/2014
8173(64*10^54467+287)/954468Robert Price04/2016
81745^77907-2*3^7790754455Mike Oakes11/2009
817520^41853-562354453Enzo Doria03/2013
817614^47506-7554448Lelio R Paula02/2013
81772^180839-11343754438Enzo Doria08/2014
81783^114085+2854433Lelio R Paula10/2012
8179Phi(141230,10)54432Ray Chandler08/2009
81806^69946-5554429Lelio R Paula10/2012
81815*2^180796+354426Lelio R Paula03/2014
8182(23*2^180782-1)/9154421Lelio R Paula01/2014
81839*6^69928-754416Lelio R Paula09/2014
818492^27701-91^2770154399Robert Price08/2015
8185(2^180687-3)*6-754393Gilbert Mozzo04/2016
8186(5*10^54388-11)/354389Erik Branger12/2013
818720^41799-304354382Enzo Doria03/2013
818813860^8387+8387^1386054382Hans Havermann08/2016
8189(F(19)^15017-F(18)^15017)/F(17)54378Wayne Halsdorf05/2010
81907^64329-1854365Lelio R Paula10/2012
81912^180551-96754352Yves Minet01/2012
819215^46209-7454347Lelio R Paula02/2013
819310^54345+2973954346Patrick De Geest08/2013
819410^54345-14138154345Patrick De Geest09/2013
8195lucasU(2098,1,16360)-lucasU(2098,1,16359)54342Mike Oakes05/2009
81962^180496+1554335Lelio R Paula02/2011
81971845^16636+16636^184554334Serge Batalov05/2014
819811^52169-7054329Lelio R Paula01/2013
819913693^9262+9262^1369354317Hans Havermann06/2016
82002^180429-11310154315Enzo Doria07/2014
82012^180423-11205154313Enzo Doria05/2014
820216112^2349+2349^1611254312Hans Havermann06/2016
8203(13^48751+4^48751)/1754305Robert Price05/2013
82042^180370+1291554297Lelio R Paula09/2012
8205(10^54290+41)/354290Robert Price01/2017
820615108^3917+3917^1510854283Hans Havermann06/2016
82072^180317-301954281Yves Minet10/2014
82082^180314+85554280Lelio R Paula10/2009
820919^42425+9454252Lelio R Paula02/2013
82102^180180-100544954240Paul Bourdelais11/2012
82112^180173-277354238Yves Minet07/2014
821213367^11418+11418^1336754238Hans Havermann06/2016
8213427^20614+20614^42754224Norbert Schneider06/2016
82142^180124-8795954223Gary Barnes08/2009
82152^180111-11310154219Enzo Doria07/2014
82162^180101-11487154216Enzo Doria05/2015
8217(11*2^180099+1)/5161754212Lelio R Paula07/2012
82192^180070+46554207Lelio R Paula09/2012
821813683^9154+9154^1368354207Hans Havermann06/2016
8220810522513*2^180009-9531*2^9531-154198Jiong Sun12/2003
82212^180014+61354190Jason Earls04/2008
82222^180007+10154188Lelio R Paula02/2011
82232^180001+4187754186Jim Fougeron08/2002
82242^180000+13015354186Jim Fougeron09/2002
82253^113565-7454185Lelio R Paula10/2012
822650^31891-4954182Norbert Schneider07/2014
8227(5*2^179991-1)/1142754180Lelio R Paula01/2014
82283^113548+2654177Lelio R Paula10/2012
8229(lucasV(1,2,360029)-2)/(3^3*522251*725981)54177Mike Oakes04/2017
82304159^14969-13854173Enzo Doria07/2012
82312^179955+577554172Lelio R Paula10/2009
82322^179953-23131354172Enzo Doria05/2014
82335^77485+654160Lelio R Paula10/2012
823418^43141+8554154Lelio R Paula02/2013
82353^113489-34054149Lelio R Paula10/2012
82367^64070+9054146Lelio R Paula10/2012
823718^43131+7154142Lelio R Paula02/2013
82382^179826-13154134Lelio R Paula02/2011
82392^179815-11273554130Enzo Doria06/2014
82402^179806+7384954127Enzo Doria04/2016
82412^179790+3354123Donovan Johnson02/2006
824214287^6138+6138^1428754120Hans Havermann06/2016
8243(17*10^54117+1)/954118Serge Batalov05/2010
82442^179763-18954115Lelio R Paula02/2011
8245(21181*2^179770+1)/302910554115Lelio R Paula05/2014
82461828^16589+16589^182854113Serge Batalov05/2014
824820^41588-588354108Enzo Doria03/2013
824750^31847-4954108Norbert Schneider07/2014
82492^179733-685554106Lelio R Paula10/2009
825020^41584-558354103Enzo Doria03/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 24 2017 22:44 (Time in France)

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